IJPAM: Volume 44, No. 3 (2008)

MULTIPLIERS FOR A QUOTIENT BANACH SPACE
AND THE NEVANLINNA-PICK THEOREM

Takahiko Nakazi
Department of Mathematics
Faculty of Science
Hokkaido University
Sapporo, 060-0810, JAPAN
e-mail: nakazi@math.hokudai.ac.jp


Abstract.Let $E$ be a Banach space on a set $X$ and $M(E)$ the space of multipliers of $E$. In this paper, we study the space of multipliers of the quotient space $E/K$, where $K$ is a closed $M(E)$ - invariant subspace in $E$. When $E$ is the classical Hilbert-Hardy space, the Nevanlinna-Pick Theorem shows $M(E/K)$ is a quotient algebra of $M(E)$.

Received: February 24, 2008

AMS Subject Classification: 47A20, 46J15

Key Words and Phrases: quotient Bahach space, multiplier, Nevanlinna-Pick Theorem, Hardy space

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 44
Issue: 3